m23 Moment of Inertia (1)

m23 Moment of Inertia (1) - MATH023 Moment of Inertia...

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MATH023 Moment of Inertia

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Objectives At the end of the period, you should be able to: Compute the moment of inertia of plane regions. Compute the moment of inertia of solids of revolution.
The strength of structural members depends to a large extent on the properties of their cross sections, particularly on the second moments, or moments of inertia, of their areas.

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Moment of Inertia Moments of inertia are used in courses such as mechanics of materials, dynamics, and fluid mechanics . The moment of inertia of an object is a measure of its resistance to change in rotation. Calculating stresses in beams – they are at times related to the moment of inertia of the cross- sectional area of the beam (resistance to bending) Mathematically, this is represented by the large wheel having a larger moment of inertia.
Moment of Inertia Moments of inertia are used in various engineering calculations, including. Locating the resultant of hydrostatic pressure forces on submerged bodies. Everyday experience tells us that it is harder to start (or stop) a large wheel turning than a small wheel. Mass moments of inertia are used in studying the rotational motion of objects.

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Moment of Inertia Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr 2 . That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.
Moment of Inertia For a point mass:

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Moment of Inertia The general form of the moment of inertia involves an integral ..
Moment of Inertia Definition: If M denotes the total mass of the system, the positive number k defined by the equation is called the radius of gyration of M with respect to the axis

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Moment of Inertia Example: If masses of 2 and 3 units are located at points (1,2) and (0,3) respectively, find the moment of inertia w.r.t. x-axis and w.r.t. y-axis. Find also the radius of gyration Given masses of 2, 4, and 5 units located at points (3,-2,3), (0,1,2), and (2,-2,4) respectively, find I x , I y and I z . Find also the radii of gyration
Moment of Inertia Example: For a rectangular area: 3 3 1 0 2 2 bh bdy y dA y I h x

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This note was uploaded on 12/08/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at Adrian College.

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m23 Moment of Inertia (1) - MATH023 Moment of Inertia...

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